Kernel Author:
Bhishan Poudel, Ph.D Contd. Astrophysics

Update: Jan 17, 2020 Fri
Date    : Jan 13, 2020

Introduction

Update

  1. Looked at gm0 vs gc0 (and gm1 vs gc1) 45 degree line and removed outliers.
  2. Find the weights for g_sq for given magnitude bins using smooth fitting curve.

Usual Filtering

df = df.query('calib_psfCandidate == 0.0')
df = df.query('deblend_nChild == 0.0')
df['ellip'] = np.hypot( df['ext_shapeHSM_HsmShapeRegauss_e1'] ,
                        df['ext_shapeHSM_HsmShapeRegauss_e2'] )
df = df.query('ellip < 2.0') # it was 1.5 before

#select only few columns after filtering:
cols_select = ['base_SdssCentroid_x', 'base_SdssCentroid_y',
                'base_SdssCentroid_xSigma','base_SdssCentroid_ySigma',
                'ext_shapeHSM_HsmShapeRegauss_e1','ext_shapeHSM_HsmShapeRegauss_e2',
                'base_SdssShape_flux']
df = df[cols_select]        

# drop all nans
df = df.dropna()

# additional columns
df['radius'] =  df.eval(""" ( (ext_shapeHSM_HsmSourceMoments_xx *  ext_shapeHSM_HsmSourceMoments_yy) \
                                          -  (ext_shapeHSM_HsmSourceMoments_xy**2 ) )**0.25 """)

Shape filtering
https://github.com/LSSTDESC/DC2-analysis/blob/master/tutorials/object_gcr_2_lensing_cuts.ipynb

df = df.query('ext_shapeHSM_HsmShapeRegauss_resolution >= 0.3')
df = df.query('ext_shapeHSM_HsmShapeRegauss_sigma <= 0.4')
df = df.query('ext_shapeHSM_HsmShapeRegauss_flag== 0.0')

Filter strongly lensed objects

  • Take the objects with centroids >154 pixels (remove strong lens objects).
    # exclude strong lens objects <=154 distance
    # The shape of lsst.fits file is 3998,3998 and center is 1699,1699.
    df['x_center'] = 1699
    df['y_center'] = 1699
    df['distance'] = ( (df['x[0]'] - df['x_center'])**2 + (df['x[1]'] - df['y_center'])**2 )**0.5
    df = df[df.distance > 154]
    

Imcat script

# create new columns and cleaning (four files)
lc -C -n fN -n id -N '1 2 x' -N '1 2 errx' -N '1 2 g' -n ellip -n flux -n radius < "${M9T}".txt  |  lc +all 'mag = %flux log10 -2.5 *'  |  cleancat 15  |  lc +all -r 'mag' > "${M9C}".cat


# merge 4 catalogs
mergecats 5 "${MC}".cat "${M9C}".cat "${LC}".cat "${L9C}".cat > ${catalogs}/merge.cat &&


lc -b +all 
'x = %x[0][0] %x[1][0] + %x[2][0] + %x[3][0] + 4 / %x[0][1] %x[1][1] + %x[2][1] + %x[3][1] + 4 / 2 vector'
'gm = %g[0][0] %g[1][0] + 2 / %g[0][1] %g[1][1] + 2 / 2 vector' 
'gc = %g[2][0] %g[3][0] + 2 / %g[2][1] %g[3][1] + 2 / 2 vector'   
'gmd = %g[0][0] %g[1][0] - 2 / %g[0][1] %g[1][1] - 2 / 2 vector' 
'gcd = %g[2][0] %g[3][0] - 2 / %g[2][1] %g[3][1] - 2 / 2 vector' 
< ${catalogs}/merge.cat > ${final}/final_${i}.cat

Notes

final_text.txt is created by imcat program after merging four lsst files (m,m9,l,l9) after cleaning.

Imports

In [1]:
import json, os,sys
import numpy as np
import pandas as pd
import seaborn as sns
import time
sns.set(color_codes=True)

import plotly
import ipywidgets

pd.set_option('display.max_columns',200)
time_start_notebook = time.time()

import matplotlib.pyplot as plt
plt.style.use('ggplot')
%matplotlib inline

print([(x.__name__, x.__version__) for x in [np,pd,sns,plotly,ipywidgets]])
[('numpy', '1.16.4'), ('pandas', '0.25.3'), ('seaborn', '0.9.0'), ('plotly', '4.4.1'), ('ipywidgets', '7.4.2')]
In [2]:
%%javascript
IPython.OutputArea.auto_scroll_threshold = 9999;

Useful Scripts

In [3]:
def show_method_attributes(obj, ncols=7,start=None, inside=None):
    """ Show all the attributes of a given method.
    Example:
    ========
    show_method_attributes(list)
     """

    print(f'Object Type: {type(obj)}\n')
    lst = [elem for elem in dir(obj) if elem[0]!='_' ]
    lst = [elem for elem in lst 
           if elem not in 'os np pd sys time psycopg2'.split() ]

    if isinstance(start,str):
        lst = [elem for elem in lst if elem.startswith(start)]
        
    if isinstance(start,tuple) or isinstance(start,list):
        lst = [elem for elem in lst for start_elem in start
               if elem.startswith(start_elem)]
        
    if isinstance(inside,str):
        lst = [elem for elem in lst if inside in elem]
        
    if isinstance(inside,tuple) or isinstance(inside,list):
        lst = [elem for elem in lst for inside_elem in inside
               if inside_elem in elem]

    return pd.DataFrame(np.array_split(lst,ncols)).T.fillna('')

Load the final text cleancat15 data

g_sq = g00 g00 + g10 g10
gmd_sq = gmd0**2 + gmd1**2
In [4]:
!head -2 ../data/cleancat/final_text_cleancat15_100.txt
head: ../data/cleancat/final_text_cleancat15_100.txt: No such file or directory
In [5]:
names = "fN[0][0]       fN[1][0]       fN[2][0]       fN[3][0]       id[0][0]       id[1][0]       id[2][0]       id[3][0]           x[0]           x[1]     errx[0][0]     errx[0][1]     errx[1][0]     errx[1][1]     errx[2][0]     errx[2][1]     errx[3][0]     errx[3][1]        g[0][0]        g[0][1]        g[1][0]        g[1][1]        g[2][0]        g[2][1]        g[3][0]        g[3][1]    ellip[0][0]    ellip[1][0]    ellip[2][0]    ellip[3][0]     flux[0][0]     flux[1][0]     flux[2][0]     flux[3][0]   radius[0][0]   radius[1][0]   radius[2][0]   radius[3][0]      mag[0][0]      mag[1][0]      mag[2][0]      mag[3][0]          gm[0]          gm[1]          gc[0]          gc[1]         gmd[0]         gmd[1]         gcd[0]         gcd[1]"
print(names)
fN[0][0]       fN[1][0]       fN[2][0]       fN[3][0]       id[0][0]       id[1][0]       id[2][0]       id[3][0]           x[0]           x[1]     errx[0][0]     errx[0][1]     errx[1][0]     errx[1][1]     errx[2][0]     errx[2][1]     errx[3][0]     errx[3][1]        g[0][0]        g[0][1]        g[1][0]        g[1][1]        g[2][0]        g[2][1]        g[3][0]        g[3][1]    ellip[0][0]    ellip[1][0]    ellip[2][0]    ellip[3][0]     flux[0][0]     flux[1][0]     flux[2][0]     flux[3][0]   radius[0][0]   radius[1][0]   radius[2][0]   radius[3][0]      mag[0][0]      mag[1][0]      mag[2][0]      mag[3][0]          gm[0]          gm[1]          gc[0]          gc[1]         gmd[0]         gmd[1]         gcd[0]         gcd[1]
In [6]:
names = ['fN[0][0]','fN[1][0]','fN[2][0]','fN[3][0]',
 'id[0][0]','id[1][0]','id[2][0]','id[3][0]',
 'x[0]','x[1]',
 'errx[0][0]','errx[0][1]','errx[1][0]','errx[1][1]','errx[2][0]',
 'errx[2][1]','errx[3][0]','errx[3][1]',
 'g[0][0]','g[0][1]','g[1][0]','g[1][1]','g[2][0]','g[2][1]','g[3][0]','g[3][1]',
 'ellip[0][0]','ellip[1][0]','ellip[2][0]','ellip[3][0]',
 'flux[0][0]','flux[1][0]','flux[2][0]','flux[3][0]',
 'radius[0][0]','radius[1][0]','radius[2][0]','radius[3][0]',
 'mag[0][0]','mag[1][0]','mag[2][0]','mag[3][0]',
 'gm[0]','gm[1]','gc[0]', 'gc[1]',
 'gmd[0]','gmd[1]','gcd[0]','gcd[1]']


file_path = '../data/cleancat/final_text_cleancat15_000_099.txt'


df = pd.read_csv(file_path,comment='#',engine='python',sep=r'\s\s+',
                 header=None,names=names)

print(df.shape)

# new columns
# df['g_sq'] = df['g[0][0]'] **2 + df['g[1][0]']**2 # only for imcat 00 and 10
# df['gmd_sq'] = df['gmd[0]'] **2 + df['gmd[1]']**2

df['g_sq'] = df['g[0][0]'] **2 + df['g[0][1]']**2
df['gmd_sq'] = df['gmd[0]'] **2 + df['gmd[1]']**2

df['gm_sq'] = df['gm[0]']**2 + df['gm[1]']**2
df['gc_sq'] = df['gc[0]']**2 + df['gc[1]']**2

df['mag_mono'] = (df['mag[0][0]'] + df['mag[1][0]'] ) / 2
df['mag_chro'] = (df['mag[2][0]'] + df['mag[3][0]'] ) / 2

df.head()
(56861, 50)
Out[6]:
fN[0][0] fN[1][0] fN[2][0] fN[3][0] id[0][0] id[1][0] id[2][0] id[3][0] x[0] x[1] errx[0][0] errx[0][1] errx[1][0] errx[1][1] errx[2][0] errx[2][1] errx[3][0] errx[3][1] g[0][0] g[0][1] g[1][0] g[1][1] g[2][0] g[2][1] g[3][0] g[3][1] ellip[0][0] ellip[1][0] ellip[2][0] ellip[3][0] flux[0][0] flux[1][0] flux[2][0] flux[3][0] radius[0][0] radius[1][0] radius[2][0] radius[3][0] mag[0][0] mag[1][0] mag[2][0] mag[3][0] gm[0] gm[1] gc[0] gc[1] gmd[0] gmd[1] gcd[0] gcd[1] g_sq gmd_sq gm_sq gc_sq mag_mono mag_chro
0 0 0 0 0 5301 5314 5231 5117 88.17075 1847.19340 0.0196 0.0249 0.0227 0.0216 0.0200 0.0256 0.0231 0.0220 -0.4253 0.1855 0.2730 -0.3021 -0.4257 0.1904 0.2778 -0.3155 0.463994 0.407177 0.466340 0.420373 79841.4700 82737.3540 80303.9230 83923.9080 5.186953 5.293858 5.267827 5.390682 -12.255571 -12.294254 -12.261842 -12.309714 -0.07615 -0.05830 -0.07395 -0.06255 -0.34915 0.24380 -0.35175 0.25295 0.215290 0.181344 0.009198 0.009381 -12.274912 -12.285778
1 0 0 0 0 3941 3957 3897 3923 3214.45390 930.33603 0.0344 0.0212 0.0331 0.0232 0.0344 0.0212 0.0332 0.0232 0.9068 0.3231 0.7867 0.3391 0.9179 0.3265 0.7956 0.3416 0.962642 0.856671 0.974240 0.865835 33913.5470 34112.9040 33903.5430 34114.7980 4.676457 4.750963 4.675408 4.751770 -11.325933 -11.332297 -11.325613 -11.332357 0.84675 0.33110 0.85675 0.33405 0.06005 -0.00800 0.06115 -0.00755 0.926680 0.003670 0.826613 0.845610 -11.329115 -11.328985
2 0 0 0 0 1301 1310 1323 1312 2652.56650 1772.34480 0.2510 0.1715 0.1663 0.3002 0.2522 0.1715 0.1665 0.3017 0.9614 0.5881 -0.9979 -0.4635 1.0062 0.6076 -1.0206 -0.4729 1.127010 1.100289 1.175422 1.124837 3694.2411 3674.4453 3684.1640 3663.4596 4.161950 4.303319 4.159870 4.301257 -8.918813 -8.912980 -8.915847 -8.909728 -0.01825 0.06230 -0.00720 0.06735 0.97965 0.52580 1.01340 0.54025 1.270152 1.236180 0.004214 0.004588 -8.915896 -8.912788
3 0 0 0 0 3564 3564 3541 3538 2536.84490 712.48793 0.0071 0.0125 0.0071 0.0129 0.0074 0.0129 0.0074 0.0134 -1.0289 0.4499 -1.0196 0.3961 -0.9862 0.4332 -0.9816 0.3755 1.122963 1.093837 1.077150 1.050970 107866.5700 109330.9900 109214.9900 110405.2400 4.848973 4.967938 4.963241 5.096215 -12.582217 -12.596858 -12.595706 -12.607474 -1.02425 0.42300 -0.98390 0.40435 -0.00465 0.02690 -0.00230 0.02885 1.261045 0.000745 1.228017 1.131558 -12.589538 -12.601590
4 0 0 0 0 4634 4659 4569 4615 109.82575 1405.32120 0.3760 0.3919 0.2353 0.2783 0.3803 0.3949 0.2379 0.2831 0.2055 0.1655 -0.1817 -0.0868 0.2052 0.1698 -0.1773 -0.0987 0.263857 0.201368 0.266344 0.202921 3512.8911 3518.9333 3517.0462 3518.1529 4.338535 4.362407 4.374177 4.392268 -8.864162 -8.866028 -8.865445 -8.865787 0.01190 0.03935 0.01395 0.03555 0.19360 0.12615 0.19125 0.13425 0.069621 0.053395 0.001690 0.001458 -8.865095 -8.865616

Plot g-squared for monochromatic and chromatic files

In [7]:
fig,ax = plt.subplots(1,2,figsize=(14,6))

df['gm_sq'].plot.hist(bins=50,ax=ax[0],color='b',label='mono')
ax[0].set_xlabel('gm_sq')
ax[0].legend()
ax[0].set_title('g-squared histogram for mono')

# gcsq
df['gc_sq'].plot.hist(bins=50,ax=ax[1],color='r',label='chro')
ax[1].set_xlabel('gc_sq')
ax[1].legend()
ax[1].set_title('g-squared histogram for chro')

# savefig
plt.savefig('images/gmsq_gcsq_hist.png')
In [8]:
plt.figure(figsize=(12,8))
sns.distplot(df['g_sq'],label='g_sq')
sns.distplot(df['gmd_sq'],label='gmd_sq')

plt.legend()
Out[8]:
<matplotlib.legend.Legend at 0x109c7d7f0>

Contour Plots

In [9]:
import plotly
import plotly.graph_objs as go
import plotly.figure_factory as ff
import plotly.tools as tls
from plotly.offline import plot, iplot, init_notebook_mode
init_notebook_mode(connected=False)
In [10]:
def matrix_of_number_density_from_two_cols(df,xcol,ycol,N):
    """Create grid of number density of two columns
    
    - Find the absolute max from two columns.
    - Create N bins -absMax to +absMax.
    - Return a matrix of N*N shape.
    """
    from itertools import product
    
    # derived variables
    xlabel = xcol
    ylabel = ycol
    xlabel1 = xlabel + '_cat_labels'
    ylabel1 = ylabel + '_cat_labels'
    
    xlabel2 = xlabel + '_cat'
    ylabel2 = ylabel + '_cat'
    colname = 'cat_freq'
    
    # take only xlabel and ylabel columns
    dx = df[[xlabel, ylabel]].copy()
    
    # get absolute maximum from two columns
    tolerance = 0.0000001
    max_abs_xcol_ycol = df[[xcol,ycol]].describe().iloc[[3,-1],:].abs().max().max()
    
    # create 1d array with N+1 values to create N bins
#     bins = np.linspace(-max_abs_xcol_ycol-tolerance, max_abs_xcol_ycol+tolerance,N+1)
    bins = np.linspace(0, max_abs_xcol_ycol,N+1)

    # create N bins
    dx[xlabel1] = pd.cut(dx[xlabel], bins, labels=np.arange(N))
    dx[ylabel1] = pd.cut(dx[ylabel], bins, labels=np.arange(N))

    # count number of points in each bin
    dx[colname] = dx.groupby([xlabel1,ylabel1])[xlabel1].transform('count')

    # drop duplicates
    dx1 = dx.drop_duplicates(subset=[xlabel1,ylabel1])[[xlabel1,ylabel1,colname]]

    # use permutation to get the grid of N * N
    perms = list(product(range(N), range(N)))
    x = [i[0] for i in perms]
    y = [i[1] for i in perms]
    dx2 = pd.DataFrame({xlabel1: x, ylabel1: y, colname:0})

    # update dx2 to merge frequency values
    dx2.update(dx2.drop(colname,1).merge(dx1,how='left'))
    dx2 = dx2.astype(int)

    # z values to plot heatmap
    z = dx2[colname].values.reshape(N,N)
    z = z.T

    return z

Transform and scale the data

In [11]:
def transform_scale(z,transform='linear',scale=None):
    """Transform and scale given 1d numpy array.
    
    transform: linear, log, sqrt, sinh, arcsinh
    scale    : minmax, zscale
    
    """
    #==================================
    # linear, log, sqrt, arcsinh, sinh 
    #
    # we need linear tranform option to compare.
    if transform == 'linear':
        z = z

    if transform == 'log':
        z = np.log1p(z)
        
    if transform == 'sqrt':
        z = np.sqrt(z)

    if transform == 'sinh':
        z = np.sinh(z)
        
    if transform == 'arcsinh':
        z = np.arcsinh(z)
    
    #===============================
    # scaling minmax and zscale
    if scale== 'minmax':
        z = z / (z.max()-z.min())
    if scale == 'zscale':
        z = (z-z.mean()) / z.std()
        
    return z

plot the countours

In [12]:
def plot_contour(Z,colorscale,x1y1x2y2=None,
                 title='Contour plot',
                 xlabel='',
                 ylabel=''):
    """Plot the contour plot.

    Contour plot from given 2d array.
    
    Example:
    -----------
    z  = matrix_of_number_density_from_two_cols(df,'gsq','gmdsq',N)
    z1 = transform_scale(z,transform=transform,scale=scale)

    plot_contour(z1, colorscale='Viridis', x1y1x2y2=[10,0,99,90],
            title=f'Contour plot: {transform}+{scale}',
            xlabel='Bin number of gsq',
            ylabel='Bin number of gmsq')
    
    """

    trace1 = go.Contour(z=Z, colorscale=colorscale)
    axis_layout = dict(
        showticklabels = True
    )
    
    xaxis = {**axis_layout, **{'title':f'{xlabel}'}}
    yaxis = {**axis_layout, **{'title':f'{ylabel}'}}

    layout = go.Layout(
        width=1000,
        height=1000,
        autosize=False,
        title=f'{title} ',
        xaxis = xaxis,
        yaxis = yaxis,
    )
    

    data = [trace1]
    
    if x1y1x2y2:

        # center line 
        p2x1, p2y1 = 0,0
        p2x2, p2y2 = 99,99
        sc1 = go.Scatter(x=[p2x1,p2x2],
                         y=[p2y1,p2y2],
                         mode = 'lines+markers',
                         name = f'line ({p2x1},{p2y1}) to ({p2x2},{p2y2})')
        
        sc2 = go.Scatter(x=[x1y1x2y2[0],x1y1x2y2[2]],
                         y=[x1y1x2y2[1],x1y1x2y2[3]],
                         mode = 'lines+markers',
                         name = f'line ({x1y1x2y2[0]},{x1y1x2y2[1]}) \
                         to ({x1y1x2y2[2]},{x1y1x2y2[3]})')


        data = [trace1, sc1, sc2]

    fig = go.Figure( data=data, layout=layout )
    
    # update figure
    fig.update_layout(
    xaxis = dict(tickmode = 'linear',dtick = 5),
    yaxis = dict(tickmode = 'linear',dtick = 5),
    )

    iplot(fig)
    return None

N = 100
transform='log'
scale='zscale'


xcol,ycol = 'g_sq', 'gmd_sq'
z  = matrix_of_number_density_from_two_cols(df,xcol,ycol,N)
z1 = transform_scale(z,transform=transform,scale=scale)

plot_contour(z1, colorscale='Viridis', x1y1x2y2=[10,0,99,90],
            title=f'Contour plot: {transform}+{scale}',
            xlabel=f'Bin number of {xcol}',
            ylabel=f'Bin number of {ycol}')

Grid of N*N from g_sq and gmd_sq

In [13]:
N = 100
xcol = 'g_sq'
ycol = 'gmd_sq'
max_abs_xcol_ycol = df[[xcol,ycol]].abs().max().max()

print(max_abs_xcol_ycol)

df[df[xcol]==max_abs_xcol_ycol]
3.99436938
Out[13]:
fN[0][0] fN[1][0] fN[2][0] fN[3][0] id[0][0] id[1][0] id[2][0] id[3][0] x[0] x[1] errx[0][0] errx[0][1] errx[1][0] errx[1][1] errx[2][0] errx[2][1] errx[3][0] errx[3][1] g[0][0] g[0][1] g[1][0] g[1][1] g[2][0] g[2][1] g[3][0] g[3][1] ellip[0][0] ellip[1][0] ellip[2][0] ellip[3][0] flux[0][0] flux[1][0] flux[2][0] flux[3][0] radius[0][0] radius[1][0] radius[2][0] radius[3][0] mag[0][0] mag[1][0] mag[2][0] mag[3][0] gm[0] gm[1] gc[0] gc[1] gmd[0] gmd[1] gcd[0] gcd[1] g_sq gmd_sq gm_sq gc_sq mag_mono mag_chro
21605 38 38 38 38 6451 6450 6448 6407 2519.428 2550.8574 0.0455 0.0406 0.0467 0.0424 0.0459 0.0408 0.0473 0.0426 1.9293 0.5217 1.5932 -0.1021 1.719 0.451 1.4994 -0.1034 1.998592 1.596468 1.777178 1.502961 12487.845 12648.607 12818.484 12914.576 4.594356 4.671837 4.688169 4.746876 -10.241219 -10.255107 -10.269592 -10.2777 1.76125 0.2098 1.6092 0.1738 0.16805 0.3119 0.1098 0.2772 3.994369 0.125522 3.146018 2.619731 -10.248163 -10.273646
In [14]:
# create 1d array with N+1 values to create N bins
bins = np.linspace(0, max_abs_xcol_ycol,N+1)

# bins dict
bins_dict = {i:v for i,v in enumerate(bins)}

# create N bins
ser_ycol_bins = pd.cut(df[ycol], bins=bins,)

df['g_sq_bins'] = ser_ycol_bins
df[['g_sq','g_sq_bins']].head()
Out[14]:
g_sq g_sq_bins
0 0.215290 (0.16, 0.2]
1 0.926680 (0.0, 0.0399]
2 1.270152 (1.198, 1.238]
3 1.261045 (0.0, 0.0399]
4 0.069621 (0.0399, 0.0799]
In [15]:
# bin 0  ==> 0          to 0.03994369
# bin 1  ==> 0.03994369 to 0.07988739
# bin 10 ==> 0.39943694 to 0.43938063

bins[10], bins[11]
Out[15]:
(0.399436938, 0.4393806318)

Analysis of Points above gmd_sq bin number 10

What is the corresponding gmsq value to y-axis bin number 10 (11th bin)?

The 100*100 bin is created from absMax of g_sq and gmd_sq. Then the line 0 to absMax is divided into 100 parts and bins are created.

bin 10 for gmd_sq is 0.39943694 to 0.43938063

In [16]:
# take all points where gmd_sq > 10th bin

df_gmd_sq_lt_bin10 = df[df.gmd_sq > bins[10]]

print(df_gmd_sq_lt_bin10.shape)

df_gmd_sq_lt_bin10.head()
(14158, 57)
Out[16]:
fN[0][0] fN[1][0] fN[2][0] fN[3][0] id[0][0] id[1][0] id[2][0] id[3][0] x[0] x[1] errx[0][0] errx[0][1] errx[1][0] errx[1][1] errx[2][0] errx[2][1] errx[3][0] errx[3][1] g[0][0] g[0][1] g[1][0] g[1][1] g[2][0] g[2][1] g[3][0] g[3][1] ellip[0][0] ellip[1][0] ellip[2][0] ellip[3][0] flux[0][0] flux[1][0] flux[2][0] flux[3][0] radius[0][0] radius[1][0] radius[2][0] radius[3][0] mag[0][0] mag[1][0] mag[2][0] mag[3][0] gm[0] gm[1] gc[0] gc[1] gmd[0] gmd[1] gcd[0] gcd[1] g_sq gmd_sq gm_sq gc_sq mag_mono mag_chro g_sq_bins
2 0 0 0 0 1301 1310 1323 1312 2652.56650 1772.3448 0.2510 0.1715 0.1663 0.3002 0.2522 0.1715 0.1665 0.3017 0.9614 0.5881 -0.9979 -0.4635 1.0062 0.6076 -1.0206 -0.4729 1.127010 1.100289 1.175422 1.124837 3694.2411 3674.4453 3684.164 3663.4596 4.161950 4.303319 4.159870 4.301257 -8.918813 -8.912980 -8.915847 -8.909728 -0.01825 0.06230 -0.00720 0.06735 0.97965 0.52580 1.01340 0.54025 1.270152 1.236180 0.004214 0.004588 -8.915896 -8.912788 (1.198, 1.238]
5 0 0 0 0 5592 1389 5393 1394 1668.12470 1882.8265 0.0453 0.0393 0.0394 0.0218 0.0457 0.0395 0.0393 0.0218 0.2646 0.9514 0.8981 -0.2964 0.2685 0.9593 0.9048 -0.3017 0.987510 0.945747 0.996167 0.953775 49474.3730 45594.8360 49496.897 45655.9450 5.496548 5.503342 5.499099 5.507981 -11.735951 -11.647289 -11.736445 -11.648743 0.58135 0.32750 0.58665 0.32880 -0.31675 0.62390 -0.31815 0.63050 0.975175 0.489582 0.445224 0.452268 -11.691620 -11.692594 (0.479, 0.519]
8 0 0 0 0 5895 5967 5826 5909 1448.97510 2334.9766 0.0188 0.0227 0.0239 0.0182 0.0189 0.0229 0.0241 0.0183 -0.2900 0.9268 0.6441 -0.7562 -0.3066 0.9498 0.6584 -0.7697 0.971112 0.993329 0.998060 1.012881 44277.4560 44510.9310 44328.676 44646.1230 4.390932 4.486290 4.404279 4.505218 -11.615457 -11.621167 -11.616712 -11.624459 0.17705 0.08530 0.17590 0.09005 -0.46705 0.84150 -0.48250 0.85975 0.943058 0.926258 0.038623 0.039050 -11.618312 -11.620586 (0.919, 0.959]
16 0 0 0 0 1916 1935 1936 1936 987.00513 2672.3523 0.0075 0.0098 0.0099 0.0079 0.0075 0.0098 0.0100 0.0079 -0.4763 0.8956 0.6350 -0.8553 -0.5089 0.9281 0.6544 -0.8827 1.014377 1.065253 1.058465 1.098817 91854.4360 93143.4830 91915.122 93209.8860 4.097640 4.188533 4.106857 4.199608 -12.407750 -12.422881 -12.408467 -12.423655 0.07935 0.02015 0.07275 0.02270 -0.55565 0.87545 -0.58165 0.90540 1.028961 1.075160 0.006702 0.005808 -12.415316 -12.416061 (1.039, 1.078]
17 0 0 0 0 4798 1156 4737 1155 1993.05820 1545.4589 0.0838 0.0597 0.0636 0.1048 0.0842 0.0598 0.0637 0.1052 1.0009 -0.3474 -0.7955 0.6838 1.0567 -0.3781 -0.8061 0.6933 1.059475 1.049001 1.122308 1.063232 10896.1520 10999.3280 10882.732 10990.3080 4.145457 4.541074 4.145158 4.539750 -10.093183 -10.103415 -10.091845 -10.102525 0.10270 0.16820 0.12530 0.15760 0.89820 -0.51560 0.93140 -0.53570 1.122488 1.072607 0.038839 0.040538 -10.098299 -10.097185 (1.039, 1.078]
In [17]:
# fN[0][0]  ==> lsst_mono_z1.5_000.fits
# fN[1][0]  ==> lsst_mono90_z1.5_000.fits
#
# id[0][0]  ==> id of given object for mono file number 0
In [18]:
# take only first file number 0 (it has m,m9,c and c9)

df_gmd_sq_lt_bin10_file0 = df_gmd_sq_lt_bin10[df_gmd_sq_lt_bin10['fN[0][0]'] == 0]

# add radius for mono
df_gmd_sq_lt_bin10_file0['radius_mono'] = \
(df_gmd_sq_lt_bin10_file0['radius[0][0]'] + 
 df_gmd_sq_lt_bin10_file0['radius[1][0]'] ) /2.0

print(df_gmd_sq_lt_bin10_file0.shape)

df_gmd_sq_lt_bin10_file0.head()
(120, 58)
Out[18]:
fN[0][0] fN[1][0] fN[2][0] fN[3][0] id[0][0] id[1][0] id[2][0] id[3][0] x[0] x[1] errx[0][0] errx[0][1] errx[1][0] errx[1][1] errx[2][0] errx[2][1] errx[3][0] errx[3][1] g[0][0] g[0][1] g[1][0] g[1][1] g[2][0] g[2][1] g[3][0] g[3][1] ellip[0][0] ellip[1][0] ellip[2][0] ellip[3][0] flux[0][0] flux[1][0] flux[2][0] flux[3][0] radius[0][0] radius[1][0] radius[2][0] radius[3][0] mag[0][0] mag[1][0] mag[2][0] mag[3][0] gm[0] gm[1] gc[0] gc[1] gmd[0] gmd[1] gcd[0] gcd[1] g_sq gmd_sq gm_sq gc_sq mag_mono mag_chro g_sq_bins radius_mono
2 0 0 0 0 1301 1310 1323 1312 2652.56650 1772.3448 0.2510 0.1715 0.1663 0.3002 0.2522 0.1715 0.1665 0.3017 0.9614 0.5881 -0.9979 -0.4635 1.0062 0.6076 -1.0206 -0.4729 1.127010 1.100289 1.175422 1.124837 3694.2411 3674.4453 3684.164 3663.4596 4.161950 4.303319 4.159870 4.301257 -8.918813 -8.912980 -8.915847 -8.909728 -0.01825 0.06230 -0.00720 0.06735 0.97965 0.52580 1.01340 0.54025 1.270152 1.236180 0.004214 0.004588 -8.915896 -8.912788 (1.198, 1.238] 4.232634
5 0 0 0 0 5592 1389 5393 1394 1668.12470 1882.8265 0.0453 0.0393 0.0394 0.0218 0.0457 0.0395 0.0393 0.0218 0.2646 0.9514 0.8981 -0.2964 0.2685 0.9593 0.9048 -0.3017 0.987510 0.945747 0.996167 0.953775 49474.3730 45594.8360 49496.897 45655.9450 5.496548 5.503342 5.499099 5.507981 -11.735951 -11.647289 -11.736445 -11.648743 0.58135 0.32750 0.58665 0.32880 -0.31675 0.62390 -0.31815 0.63050 0.975175 0.489582 0.445224 0.452268 -11.691620 -11.692594 (0.479, 0.519] 5.499945
8 0 0 0 0 5895 5967 5826 5909 1448.97510 2334.9766 0.0188 0.0227 0.0239 0.0182 0.0189 0.0229 0.0241 0.0183 -0.2900 0.9268 0.6441 -0.7562 -0.3066 0.9498 0.6584 -0.7697 0.971112 0.993329 0.998060 1.012881 44277.4560 44510.9310 44328.676 44646.1230 4.390932 4.486290 4.404279 4.505218 -11.615457 -11.621167 -11.616712 -11.624459 0.17705 0.08530 0.17590 0.09005 -0.46705 0.84150 -0.48250 0.85975 0.943058 0.926258 0.038623 0.039050 -11.618312 -11.620586 (0.919, 0.959] 4.438611
16 0 0 0 0 1916 1935 1936 1936 987.00513 2672.3523 0.0075 0.0098 0.0099 0.0079 0.0075 0.0098 0.0100 0.0079 -0.4763 0.8956 0.6350 -0.8553 -0.5089 0.9281 0.6544 -0.8827 1.014377 1.065253 1.058465 1.098817 91854.4360 93143.4830 91915.122 93209.8860 4.097640 4.188533 4.106857 4.199608 -12.407750 -12.422881 -12.408467 -12.423655 0.07935 0.02015 0.07275 0.02270 -0.55565 0.87545 -0.58165 0.90540 1.028961 1.075160 0.006702 0.005808 -12.415316 -12.416061 (1.039, 1.078] 4.143086
17 0 0 0 0 4798 1156 4737 1155 1993.05820 1545.4589 0.0838 0.0597 0.0636 0.1048 0.0842 0.0598 0.0637 0.1052 1.0009 -0.3474 -0.7955 0.6838 1.0567 -0.3781 -0.8061 0.6933 1.059475 1.049001 1.122308 1.063232 10896.1520 10999.3280 10882.732 10990.3080 4.145457 4.541074 4.145158 4.539750 -10.093183 -10.103415 -10.091845 -10.102525 0.10270 0.16820 0.12530 0.15760 0.89820 -0.51560 0.93140 -0.53570 1.122488 1.072607 0.038839 0.040538 -10.098299 -10.097185 (1.039, 1.078] 4.343265

Regions above and below for gsq vs gmdsq contour plot

For example, take points:
Lower line below the diagonal line
point on x-axis: x1,y1 = 10,0
point on y-axis: x2,y2 = 99,90

here 20,0,99,80 are bin number, their values are obtained from bins_dict
x1,y1 = bins_dict[10], bins_dict[0]
x2,y2 = bins_dict[99], bins_dict[90]


Equation of straight line:
y-y1 = y2-y1 * (x-x1)
       -----
       x2-x1

boundary: (x2-x1) * (y-y1) - (y2-y1) * (x-x1)
In [19]:
N = 100
bins = np.linspace(0, max_abs_xcol_ycol,N+1)
bins_dict = {i:v for i,v in enumerate(bins)}

# points from contour plot
x1y1x2y2 = [10,0,99,90]
print(x1y1x2y2)

# actual values of x1, y1, x2, and y2
x1,y1 = bins_dict[x1y1x2y2[0]], bins_dict[x1y1x2y2[1]]
x2,y2 = bins_dict[x1y1x2y2[2]], bins_dict[x1y1x2y2[3]]


df['above'] = df.eval(" ( (@x2-@x1) * gmd_sq )  >= ( (@y2-@y1) * (g_sq - @x1 )) ")


print(df['above'].value_counts())
print()
print(df['above'].value_counts(normalize=True))
[10, 0, 99, 90]
True     31077
False    25784
Name: above, dtype: int64

True     0.546543
False    0.453457
Name: above, dtype: float64
In [20]:
df[df.above==True]['gm_sq'].plot.hist(figsize=(12,8),bins=60,color='b',label='Above')

nabove = len(df[df.above==True])
nbelow = len(df[df.above==False])

above_pct = nabove/(nabove+nbelow)*100
below_pct = 100-above_pct
text = f'Above = {nabove:,} ({above_pct:,.0f}%)\nBelow = {nbelow:,} ( {below_pct:,.0f}%)'

plt.text(0.5,10_000,text,fontsize=14)
plt.legend()

plt.xlabel('gm_sq')
plt.title('gm_sq histograms for above and below cases', fontsize=20)

df[df.above==False]['gm_sq'].plot.hist(figsize=(12,8),bins=60,color='r',alpha=0.5,label='Below')
plt.legend()
plt.xlabel('gm_sq')
plt.title('gm_sq histograms below the boundary', fontsize=20)
Out[20]:
Text(0.5, 1.0, 'gm_sq histograms below the boundary')
In [21]:
df[df.above==True]['gm_sq'].plot.hist(figsize=(12,8),bins=60,color='r',alpha=0.5)
plt.xlabel('gm_sq')
plt.title('gm_sq histogram', fontsize=20)
Out[21]:
Text(0.5, 1.0, 'gm_sq histogram')
In [22]:
df[df.above==False]['gm_sq'].plot.hist(figsize=(12,8),bins=60,color='r',alpha=0.5,label='Below')
plt.legend()
plt.xlabel('gm_sq')
plt.title('gm_sq histograms below the boundary', fontsize=20)
Out[22]:
Text(0.5, 1.0, 'gm_sq histograms below the boundary')

Now, Take only the data above the boundary as cleaned data

In [23]:
rows_before = df.shape[0]
df = df[df.above==True]

print(f'Before rows: {rows_before}, After rows: {df.shape[0]}')
Before rows: 56861, After rows: 31077
In [24]:
plt.figure(figsize=(12,8))
sns.distplot(df['gm_sq'],label='gm_sq')
plt.legend()
plt.savefig('images/gmsq_histogram_after_cleaning.png',dpi=300)

gm vs gc Plots

Equation of straight line:
y-y1 = y2-y1 * (x-x1)
       -----
       x2-x1

boundary: (x2-x1) * (y-y1) - (y2-y1) * (x-x1)
In [25]:
fig,ax = plt.subplots(1,2,figsize=(16,8))
df.plot.scatter(x='gm[0]',y='gc[0]', ax=ax[0])
df.plot.scatter(x='gm[1]',y='gc[1]', ax=ax[1])

ax[0].set_xlim(-2.0,2.0)
ax[0].set_ylim(-2.0,2.0)

ax[1].set_xlim(-2.0,2.0)
ax[1].set_ylim(-2.0,2.0)

# 45 degree line
n=2.0
ax[0].plot([-n,n],[-n,n],'r--')
ax[1].plot([-n,n],[-n,n],'r--')

plt.suptitle('gm vs gc plot',weight='bold',fontsize=24);

Remove outliers based on gm vs gc plot

In [26]:
# Two scatter plots
#===========================================
fig,ax = plt.subplots(1,2,figsize=(16,8))
plt.suptitle('gm vs gc plot',weight='bold',fontsize=24);

df.plot.scatter(x='gm[0]',y='gc[0]', ax=ax[0])
df.plot.scatter(x='gm[1]',y='gc[1]', ax=ax[1])

ax[0].set_xlim(-2.0,2.0)
ax[0].set_ylim(-2.0,2.0)

ax[1].set_xlim(-2.0,2.0)
ax[1].set_ylim(-2.0,2.0)

# 45 degree line
n=2.0
ax[0].plot([-n,n],[-n,n],'r--')
ax[1].plot([-n,n],[-n,n],'r--')



# Left plot gm0 vs gc0 parallel lines
#===========================================
x = df['gm[0]'].to_numpy()
y = df['gc[0]'].to_numpy()

# Find distance for parallel lines
sigma = (x - y).std()
n = 10
d = n * sigma
c = d/np.sqrt(2) 
y1 = x + c
y2 = x - c

# left plot parallel lines
ax[0].plot(y1,x,'b-.',label=f'{n} sigma')
ax[0].plot(y2,x,'b-.')


# Right plot gm1 vs gc1 parallel lines
#===========================================
x = df['gm[1]'].to_numpy()
y = df['gc[1]'].to_numpy()

sigma = (x - y).std()
n = 10
d = n * sigma
c = d/np.sqrt(2) 
y1 = x + c
y2 = x - c

ax[1].plot(y1,x,'b-.', label=f'{n} sigma')
ax[1].plot(y2,x,'b-.')


#=============
# Add legends
# plt.tight_layout()
ax[0].legend(loc='upper left')
ax[1].legend(loc='upper left')

plt.show()
In [27]:
# Remove outliers for gc0 vs gm0
n = 10
sigma = (df['gm[0]'] - df['gc[0]']).std()
d = n * sigma
c = d/np.sqrt(2)

cond_upper = (df['gc[0]'] - df['gm[0]'] <= c)
cond_below = (df['gm[0]'] - df['gc[0]'] <= c)

df = df[ cond_upper & cond_below ]


# df.plot.scatter(x='gm[0]',y='gc[0]')
In [28]:
# Remove outliers for gc1 vs gm1
n = 10
sigma = (df['gm[1]'] - df['gc[1]']).std()
d = n * sigma
c = d/np.sqrt(2)

cond_upper = (df['gc[1]'] - df['gm[1]'] <= c)
cond_below = (df['gm[1]'] - df['gc[1]'] <= c)

df = df[ cond_upper & cond_below ]


# df.plot.scatter(x='gm[1]',y='gc[1]')
In [29]:
# Two scatter plots
#===========================================
fig,ax = plt.subplots(1,2,figsize=(16,8))
plt.suptitle('gm vs gc plot',weight='bold',fontsize=24);

df.plot.scatter(x='gm[0]',y='gc[0]', ax=ax[0])
df.plot.scatter(x='gm[1]',y='gc[1]', ax=ax[1])

ax[0].set_xlim(-2.0,2.0)
ax[0].set_ylim(-2.0,2.0)

ax[1].set_xlim(-2.0,2.0)
ax[1].set_ylim(-2.0,2.0)

# 45 degree line
n=2.0
ax[0].plot([-n,n],[-n,n],'r--')
ax[1].plot([-n,n],[-n,n],'r--')



# Left plot gm0 vs gc0 parallel lines
#===========================================
x = df['gm[0]'].to_numpy()
y = df['gc[0]'].to_numpy()

# Find distance for parallel lines
sigma = (x - y).std()
n = 10
d = n * sigma
c = d/np.sqrt(2) 
y1 = x + c
y2 = x - c

# left plot parallel lines
ax[0].plot(y1,x,'b-.',label=f'{n} sigma')
ax[0].plot(y2,x,'b-.')




# Right plot gm1 vs gc1 parallel lines
#===========================================
x = df['gm[1]'].to_numpy()
y = df['gc[1]'].to_numpy()

sigma = (x - y).std()
n = 10
d = n * sigma
c = d/np.sqrt(2) 
y1 = x + c
y2 = x - c

ax[1].plot(y1,x,'b-.', label=f'{n} sigma')
ax[1].plot(y2,x,'b-.')


#=============
# Add legends
# plt.tight_layout()
ax[0].legend(loc='upper left')
ax[1].legend(loc='upper left')

plt.show()

Plot magnidude for different bin numbers

In [30]:
df.filter(regex='mag').head(2)
Out[30]:
mag[0][0] mag[1][0] mag[2][0] mag[3][0] mag_mono mag_chro
0 -12.255571 -12.294254 -12.261842 -12.309714 -12.274912 -12.285778
2 -8.918813 -8.912980 -8.915847 -8.909728 -8.915896 -8.912788
In [31]:
df[['gm_sq','gc_sq']].describe()
Out[31]:
gm_sq gc_sq
count 3.091600e+04 3.091600e+04
mean 6.772525e-02 6.839417e-02
std 1.250391e-01 1.269363e-01
min 3.650000e-07 3.725000e-07
25% 4.597300e-03 4.629639e-03
50% 1.403978e-02 1.417969e-02
75% 6.022721e-02 6.076146e-02
max 1.866975e+00 1.840423e+00
In [32]:
def plot_bin_mag_mono_chro(nbins,show=False,ret=False):
    import os
    
    if not os.path.isdir('images'):
        os.makedirs('images')
    
    df['bins_mag_mono'] = pd.cut(df['mag_mono'],nbins)
    df['bins_mag_chro'] = pd.cut(df['mag_chro'],nbins)
    
    # show the text of bin counts
    text_mono = df.groupby('bins_mag_mono')['gm_sq'].agg(['count', 'mean'])
    text_mono = text_mono.reset_index().assign(pct_change = lambda x: x['mean'].pct_change())
    text_mono = text_mono.to_string().replace('mean','gm_sq')
    
    text_chro = df.groupby('bins_mag_chro')['gc_sq'].agg(['count', 'mean'])
    text_chro = text_chro.reset_index().assign(pct_change = lambda x: x['mean'].pct_change())
    text_chro = text_chro.to_string().replace('mean','gc_sq')
 
    # data to plot
    df_mono_gm_sq_mean = df.groupby('bins_mag_mono')['gm_sq'].mean()
    df_chro_gm_sq_mean = df.groupby('bins_mag_chro')['gc_sq'].mean()
    
    # plot
    fig,ax = plt.subplots(1,2,figsize=(12,8))
    
    # mono (plot the magnitude mean in each bins)
    df_mono_gm_sq_mean.plot(marker='o',ax=ax[0])
    ax[0].tick_params(axis='x', rotation=90)
    ax[0].set_ylabel('gm_sq_mean',fontsize=18)
    ax[0].set_xlabel('bin_mag_mono',fontsize=18)
    ax[0].set_title(f'gm_sq per magnitude bins with nbins = {nbins}')
    ax[0].text(0,0.5,text_mono,fontsize=14,va='center')
    ax[0].set_ylim(0,1)
    ax[0].set_yticks(np.arange(0, 1, step=0.1))
 
    # chro
    df_chro_gm_sq_mean.plot(marker='o',ax=ax[1])
    ax[1].tick_params(axis='x', rotation=90)
    ax[1].set_ylabel('gc_sq_mean',fontsize=18)
    ax[1].set_xlabel('bin_mag_chro',fontsize=18)
    ax[1].set_title(f'gc_sq per magnitude bins with nbins = {nbins}')
    ax[1].text(0,0.5,text_chro,fontsize=14,va='center')
    ax[1].set_ylim(0,1)
    ax[1].set_yticks(np.arange(0, 1, step=0.1))
    
    plt.tight_layout()
    plt.savefig(f'images/bin_mag_mono_chro_{nbins}.png')
    
    if show:
        plt.show()
    plt.close()
    
    if ret:
        return df_mono_gm_sq_mean, df_chro_gm_sq_mean

for nbins in range(5,15):
    plot_bin_mag_mono_chro(nbins,show=True)
In [33]:
"""
Note:
These plots were much different previously without doing some filterings:

https://nbviewer.jupyter.org/github/bpRsh/2019_shear_analysis_after_dmstack/blob/master/Jan_2020/a01_jan8/a01_cleancat15_gc0_gm0.ipynb

""";

Magnitude weight column for Monochromatic case

In [34]:
df['mag_mono'].plot.hist()
Out[34]:
<matplotlib.axes._subplots.AxesSubplot at 0x123465ba8>
In [35]:
nbins = 9 # the bin number looks good in above gm_sq plots
df_mono, df_chro = plot_bin_mag_mono_chro(nbins,show=True,ret=True)
In [36]:
# from plot above I can see from Kth point graph goes up.
# graph is flat upto Kth point then increases linearly to top of curve.

num_start_increasing = 3 
df_mono.index[num_start_increasing]
Out[36]:
Interval(-12.421, -11.705, closed='right')
In [37]:
# how to choose the bottom of the slope mathematically?
# try to see pct change

df_mono.pct_change().to_frame('gm_sq_pct_change').style.background_gradient(low=0,high=0.9)
/Users/poudel/miniconda3/envs/dataSc/lib/python3.7/site-packages/matplotlib/colors.py:527: RuntimeWarning:

invalid value encountered in less

Out[37]:
gm_sq_pct_change
bins_mag_mono
(-14.577, -13.854] nan
(-13.854, -13.138] 0.0209906
(-13.138, -12.421] -0.218099
(-12.421, -11.705] 0.186364
(-11.705, -10.989] 0.801036
(-10.989, -10.272] 0.414426
(-10.272, -9.556] 0.185832
(-9.556, -8.84] -0.406577
(-8.84, -8.123] -0.244134
In [38]:
# look at smaller part than
df_mono_left = df_mono.pct_change()\
    .loc[df_mono.pct_change().index < df_mono.pct_change().idxmax()]

df_mono_left
Out[38]:
bins_mag_mono
(-14.577, -13.854]         NaN
(-13.854, -13.138]    0.020991
(-13.138, -12.421]   -0.218099
(-12.421, -11.705]    0.186364
Name: gm_sq, dtype: float64
In [39]:
df_mono_left.loc[lambda x: x<0.2] # take pct change less than 0.2
Out[39]:
bins_mag_mono
(-13.854, -13.138]    0.020991
(-13.138, -12.421]   -0.218099
(-12.421, -11.705]    0.186364
Name: gm_sq, dtype: float64
In [40]:
df_mono_left.loc[lambda x: x<0.2].shape # this gives the number 3
# but this is not full-proof method, simply look at the plot and choose the
# bottom of slope visually.
Out[40]:
(3,)
In [41]:
df_mono.to_frame().style.background_gradient()
Out[41]:
gm_sq
bins_mag_mono
(-14.577, -13.854] 0.0420542
(-13.854, -13.138] 0.042937
(-13.138, -12.421] 0.0335725
(-12.421, -11.705] 0.0398292
(-11.705, -10.989] 0.0717338
(-10.989, -10.272] 0.101462
(-10.272, -9.556] 0.120317
(-9.556, -8.84] 0.071399
(-8.84, -8.123] 0.0539681
In [42]:
df_mono.index[num_start_increasing].left, df_mono.index[num_start_increasing].right
Out[42]:
(-12.421, -11.705)
In [43]:
df_mono.idxmax() # index for peak of curve
Out[43]:
Interval(-10.272, -9.556, closed='right')
In [44]:
df_mono.idxmax().left, df_mono.idxmax().right
Out[44]:
(-10.272, -9.556)
In [45]:
# look at case when nbinsK = 9 and when the curve is going up
# index for when curve goes linearly up after initial flat
idx_bottom_of_slope_mono = [df_mono.index[num_start_increasing].left,
                       df_mono.index[num_start_increasing].right
                       ]

mag_low_nbinsK_mono = np.mean(idx_bottom_of_slope_mono)

# index for peak of curve
idx_peak_mono = [df_mono.idxmax().left,
            df_mono.idxmax().right
           ]
mag_high_nbinsK_mono = np.mean(idx_peak_mono)

idx_bottom_of_slope_mono, idx_peak_mono, mag_low_nbinsK_mono, mag_high_nbinsK_mono
Out[45]:
([-12.421, -11.705], [-10.272, -9.556], -12.062999999999999, -9.914)
In [46]:
from scipy.optimize import curve_fit

xcol = 'mag_mono'
ycol = 'gm_sq'

x = df.query("""  @mag_low_nbinsK_mono < mag_mono <  @mag_high_nbinsK_mono  """)[xcol].to_numpy()
y = df.query("""  @mag_low_nbinsK_mono < mag_mono <  @mag_high_nbinsK_mono  """)[ycol].to_numpy()

def func(x, a, b):
    return a*x + b

params, _ = curve_fit(func, x, y)
[a, b] = params.round(2)

print(f'magnitude ranges for mono: {mag_low_nbinsK_mono}, {mag_high_nbinsK_mono}')
print(f'fitting params   for mono: {a}, {b}' )
magnitude ranges for mono: -12.062999999999999, -9.914
fitting params   for mono: 0.04, 0.51
In [47]:
mag_low_nbinsK_mono
Out[47]:
-12.062999999999999
In [48]:
def magnitude_weight_mono(mag):
    if mag < mag_low_nbinsK_mono:
        return 1/ (mag_low_nbinsK_mono *a + b)
    
    else:
        return 1/ (a*mag + b)

df['wt_mag_mono'] = df['mag_mono'].apply(magnitude_weight_mono)
df['wt_mag_mono'] = df['wt_mag_mono'] / df['wt_mag_mono'].mean() # normalize by mean

Magnitude weight column for Chromatic case

In [49]:
df['mag_chro'].plot.hist()
Out[49]:
<matplotlib.axes._subplots.AxesSubplot at 0x121bec198>
In [50]:
nbins = 9 # the bin number looks good in above gm_sq plots
df_mono, df_chro = plot_bin_mag_mono_chro(nbins,show=True,ret=True)
In [51]:
# from plot above I can see from Kth point graph goes up.
# graph is flat upto Kth point then increases linearly to top of curve.

num_start_increasing = 3 
df_chro.index[num_start_increasing]
Out[51]:
Interval(-12.417, -11.699, closed='right')
In [52]:
# look at case when nbinsK = 9 and when the curve is going up
# index for when curve goes linearly up after initial flat
idx_bottom_of_slope_chro = [df_chro.index[num_start_increasing].left,
                            df_chro.index[num_start_increasing].right
                            ]

mag_low_nbinsK_chro = np.mean(idx_bottom_of_slope_chro)

# index for peak of curve
idx_peak_chro = [df_chro.idxmax().left,
                 df_chro.idxmax().right
                 ]
mag_high_nbinsK_chro = np.mean(idx_peak_chro)

idx_bottom_of_slope_chro, idx_peak_chro, mag_low_nbinsK_chro, mag_high_nbinsK_chro
Out[52]:
([-12.417, -11.699], [-10.263, -9.546], -12.058, -9.904499999999999)
In [53]:
from scipy.optimize import curve_fit


xcol = 'mag_chro'
ycol = 'gc_sq'

x = df.query("""  @mag_low_nbinsK_chro < mag_chro <  @mag_high_nbinsK_chro  """)[xcol].to_numpy()
y = df.query("""  @mag_low_nbinsK_chro < mag_chro <  @mag_high_nbinsK_chro  """)[ycol].to_numpy()

def func(x, a, b):
    return a*x + b

params, _ = curve_fit(func, x, y)
[a, b] = params.round(2)

print(f'magnitude ranges for chro: {mag_low_nbinsK_chro}, {mag_high_nbinsK_chro}')
print(f'fitting params   for chro: {a}, {b}' )
magnitude ranges for chro: -12.058, -9.904499999999999
fitting params   for chro: 0.04, 0.53
In [54]:
mag_low_nbinsK_chro
Out[54]:
-12.058
In [55]:
def magnitude_weight_chro(mag):
    if mag < mag_low_nbinsK_chro:
        return 1/ (mag_low_nbinsK_chro*a + b)
    
    else:
        return 1/ (a*mag + b)

df['wt_mag_chro'] = df['mag_chro'].apply(magnitude_weight_chro)
df['wt_mag_chro'] = df['wt_mag_chro'] / df['wt_mag_chro'].mean() # normalize by mean

# mean
df['wt_mag']      = (df['wt_mag_mono'] + df['wt_mag_chro']) / 2

# df.drop(['wt_mag_chro','wt_mag_mono'],axis=1,inplace=True)

df.iloc[:2,-7:]
Out[55]:
g_sq_bins above bins_mag_mono bins_mag_chro wt_mag_mono wt_mag_chro wt_mag
0 (0.16, 0.2] True (-12.421, -11.705] (-12.417, -11.699] 1.704526 1.515862 1.610194
2 (1.198, 1.238] True (-9.556, -8.84] (-9.546, -8.828] 0.305419 0.416606 0.361013

Ellipticity Components Transformation

c2 = (dx * dx - dy * dy) / (r * r);
s2 = 2 * dx * dy / (r * r);
eX = s2 * e[0] + c2 * e[1];
eesum += eX * eX * w[0] * w[0];
eTsum[bin] -= (c2 * e[0] + s2 * e[1]) * w[0];
In [56]:
df.head(2)
Out[56]:
fN[0][0] fN[1][0] fN[2][0] fN[3][0] id[0][0] id[1][0] id[2][0] id[3][0] x[0] x[1] errx[0][0] errx[0][1] errx[1][0] errx[1][1] errx[2][0] errx[2][1] errx[3][0] errx[3][1] g[0][0] g[0][1] g[1][0] g[1][1] g[2][0] g[2][1] g[3][0] g[3][1] ellip[0][0] ellip[1][0] ellip[2][0] ellip[3][0] flux[0][0] flux[1][0] flux[2][0] flux[3][0] radius[0][0] radius[1][0] radius[2][0] radius[3][0] mag[0][0] mag[1][0] mag[2][0] mag[3][0] gm[0] gm[1] gc[0] gc[1] gmd[0] gmd[1] gcd[0] gcd[1] g_sq gmd_sq gm_sq gc_sq mag_mono mag_chro g_sq_bins above bins_mag_mono bins_mag_chro wt_mag_mono wt_mag_chro wt_mag
0 0 0 0 0 5301 5314 5231 5117 88.17075 1847.1934 0.0196 0.0249 0.0227 0.0216 0.0200 0.0256 0.0231 0.0220 -0.4253 0.1855 0.2730 -0.3021 -0.4257 0.1904 0.2778 -0.3155 0.463994 0.407177 0.466340 0.420373 79841.4700 82737.3540 80303.923 83923.9080 5.186953 5.293858 5.267827 5.390682 -12.255571 -12.294254 -12.261842 -12.309714 -0.07615 -0.0583 -0.07395 -0.06255 -0.34915 0.2438 -0.35175 0.25295 0.215290 0.181344 0.009198 0.009381 -12.274912 -12.285778 (0.16, 0.2] True (-12.421, -11.705] (-12.417, -11.699] 1.704526 1.515862 1.610194
2 0 0 0 0 1301 1310 1323 1312 2652.56650 1772.3448 0.2510 0.1715 0.1663 0.3002 0.2522 0.1715 0.1665 0.3017 0.9614 0.5881 -0.9979 -0.4635 1.0062 0.6076 -1.0206 -0.4729 1.127010 1.100289 1.175422 1.124837 3694.2411 3674.4453 3684.164 3663.4596 4.161950 4.303319 4.159870 4.301257 -8.918813 -8.912980 -8.915847 -8.909728 -0.01825 0.0623 -0.00720 0.06735 0.97965 0.5258 1.01340 0.54025 1.270152 1.236180 0.004214 0.004588 -8.915896 -8.912788 (1.198, 1.238] True (-9.556, -8.84] (-9.546, -8.828] 0.305419 0.416606 0.361013
In [57]:
# constants
RMIN = 10
DLNR = 0.5

df['dx'] = df['x[0]'] - 1699 # jesisim output fitsfiles have shape 3398, 3398
df['dy'] = df['x[1]'] - 1699

df['r'] = np.hypot(df['dx'], df['dy'])
# df['r'] = np.sqrt(df['dx']**2 + df['dy']**2)

df['cos2theta'] = df.eval(' (dx * dx - dy * dy) / (r * r)' )
df['sin2theta'] = df.eval(' (2  * dx * dy     ) / (r * r)' )

df['bin'] = ( np.log(df.r / RMIN) / DLNR).astype(int)

df['bin'].value_counts()
Out[57]:
9     12232
10    11073
8      4765
7      2001
6       707
5        79
3        35
4         8
2         6
1         5
0         5
Name: bin, dtype: int64
In [58]:
df['eX_mono'] =       df['sin2theta'] * df['gm[0]'] + df['cos2theta'] * df['gm[1]']
df['eT_mono'] = -1 * (df['cos2theta'] * df['gm[0]'] + df['sin2theta'] * df['gm[1]'] ) 

df['eX_chro'] =       df['sin2theta'] * df['gc[0]'] + df['cos2theta'] * df['gc[1]']
df['eT_chro'] = -1 * (df['cos2theta'] * df['gc[0]'] + df['sin2theta'] * df['gc[1]']  )
In [59]:
df['eT_mono_times_wt'] = df['eT_mono'] * df['wt_mag']
df['eT_chro_times_wt'] = df['eT_chro'] * df['wt_mag']
In [60]:
df['eX_mono_times_wt'] = df['eX_mono'] * df['wt_mag']
df['eX_chro_times_wt'] = df['eX_chro'] * df['wt_mag']

df['eX_times_wt'] = df.eval(" (eX_mono_times_wt + eX_chro_times_wt) / 2 ")

df.iloc[:2,-6:]
Out[60]:
eT_chro eT_mono_times_wt eT_chro_times_wt eX_mono_times_wt eX_chro_times_wt eX_times_wt
0 0.061296 0.103431 0.098699 -0.069927 -0.077302 -0.073614
2 -0.003184 0.003071 -0.001150 0.021219 0.023631 0.022425

Error Analysis

https://www.phenix.bnl.gov/WWW/publish/elke/EIC/Files-for-Wiki/lara.02-008.errors.pdf

When the statistics involved in calculating $E_A$ and $E_B$ are not indendent, the error for a function $f(E_A, E_B)$ has the expression: $$ \sigma_{f}=\sqrt{\left(\frac{\partial f}{\partial E_{A}} \sigma_{A}\right)^{2}+\left(\frac{\partial f}{\partial E_{B}} \sigma_{B}\right)^{2}+2 \frac{\partial f}{\partial E_{A}} \frac{\partial f}{\partial E_{B}} \operatorname{cov}\left(E_{A}, E_{B}\right)} $$

where the last term takes care of the correlations between $E_A$ and $E_B$. Given a large number $N$ of measurements $E_{A_i}$, the standard deviation $\sigma_A$ is empirically defined as:

$$ \sigma_{A}^{2}=\frac{1}{N-1} \sum_{i=1}^{N}\left(E_{A_{i}}-E_{A}\right)^{2} $$

while the covariance between $E_A$ and $E_B$ is given by: $$ \operatorname{cov}\left(E_{A}, E_{B}\right)=\frac{1}{N-1} \sum_{i=1}^{N}\left(E_{A_{i}}-E_{A}\right)\left(E_{B_{i}}-E_{B}\right) $$

where $E_A$ and $E_B$ are the averages of $E_{A_i}$ and $E_{B_i}$. When $E_A$ and $E_B$ are independent, over a large number $N$ of measurements they will fluctuate around their average in an uncorrelated way, so that the covariance is zero and one recovers the usual formula for the propagation of errors in a function of independent variables.

In [61]:
"""
f = m/c
df/dm = 1/c
df/dc = -m/c2

s2 ==> sigma
s2 = r2 (sm2/m2 + sc2/c2 -2/m/c cov(m,c))

put m=c,
s2 = 2/m2 (sm2 - cov)

error = sigma/sqrt(n)

error = 
            0.000332
      sqrt  --------
             eT(bin)**2
    ---------------------
     sqrt(ngals_bin)
""";
In [62]:
# temporary value to calculate error
err_coeff = 0.000332
df['err_numerator'] = np.sqrt(err_coeff/df['eT_mono']/df['eT_mono'])

df['eX_chro_times_wt_std'] = df['eX_chro_times_wt'].std()
df['eT_ratio'] = df['eT_mono'] / df['eT_chro']
df['eT_ratio_std'] = df['eT_ratio'].std()
df.iloc[:2,-5:]
Out[62]:
eX_times_wt err_numerator eX_chro_times_wt_std eT_ratio eT_ratio_std
0 -0.073614 0.283660 0.171205 1.047939 4.54445
2 0.022425 2.141634 0.171205 -2.671767 4.54445
In [63]:
df[['eT_chro','eT_mono']].cov()
Out[63]:
eT_chro eT_mono
eT_chro 0.034177 0.033831
eT_mono 0.033831 0.033817
In [64]:
df[['eT_chro','eT_mono']].cov().iloc[0,1]
Out[64]:
0.03383088524745581
In [65]:
(0.034177+0.033817)/2
Out[65]:
0.033997
In [66]:
0.033997 - (0.171205**2)
Out[66]:
0.004685847975000001
In [67]:
0.004685847975000001*2
Out[67]:
0.009371695950000002

Radial Binnings

In [68]:
# constants
RMIN = 10
DLNR = 0.5
In [69]:
# renaming aggegration needs pandas > 0.25
pd.__version__
Out[69]:
'0.25.3'
In [70]:
df_radial_bins = df.groupby('bin').agg(
    r_mean               = ('r', 'mean'),
    wt_mag_sum           = ('wt_mag', 'sum'),
    eT_mono_times_wt_sum = ('eT_mono_times_wt', 'sum'),
    eT_chro_times_wt_sum = ('eT_chro_times_wt', 'sum'),
    eX_mono_times_wt_sum = ('eX_mono_times_wt', 'sum'),
    eX_chro_times_wt_sum = ('eX_chro_times_wt', 'sum'),
    err_numerator_sum    = ('err_numerator', 'sum')
                                       )


# bin counts
df_radial_bins['bin_count'] = df['bin'].value_counts()

# columns after binning 
df_radial_bins = df_radial_bins.eval("""
    eT_mean_mono = eT_mono_times_wt_sum / wt_mag_sum
    eT_mean_chro = eT_chro_times_wt_sum / wt_mag_sum
    eX_mean_mono = eX_mono_times_wt_sum / wt_mag_sum
    eX_mean_chro = eX_chro_times_wt_sum / wt_mag_sum
    eT_ratio = eT_mean_mono / eT_mean_chro
    """
)

# Errors
b = np.sqrt(df_radial_bins['bin_count'])
df_radial_bins['eT_mono_err'] = df_radial_bins['eT_mono_times_wt_sum'] / b
df_radial_bins['eT_chro_err'] = df_radial_bins['eT_chro_times_wt_sum'] / b
df_radial_bins['eX_mono_err'] = df_radial_bins['eX_mono_times_wt_sum'] / b
df_radial_bins['eX_chro_err'] = df_radial_bins['eX_chro_times_wt_sum'] / b
df_radial_bins['eT_ratio_err'] = df_radial_bins['err_numerator_sum'] / b

print('Statistics for different radial bins')
print(f'RMIN = {RMIN} and DLNR = {DLNR}')

df_radial_bins.style\
.background_gradient(subset=['eT_mean_mono','eT_mean_chro'],cmap='Blues')
Statistics for different radial bins
RMIN = 10 and DLNR = 0.5
Out[70]:
r_mean wt_mag_sum eT_mono_times_wt_sum eT_chro_times_wt_sum eX_mono_times_wt_sum eX_chro_times_wt_sum err_numerator_sum bin_count eT_mean_mono eT_mean_chro eX_mean_mono eX_mean_chro eT_ratio eT_mono_err eT_chro_err eX_mono_err eX_chro_err eT_ratio_err
bin
0 12.4392 2.40509 -0.245264 -0.226094 -0.746423 -0.752616 0.395941 5 -0.101977 -0.0940067 -0.310352 -0.312927 1.08479 -0.109685 -0.101112 -0.333811 -0.33658 0.17707
1 21.4642 2.80779 0.0384375 0.00819027 -0.286836 -0.307534 3.01672 5 0.0136896 0.00291699 -0.102157 -0.109529 4.69307 0.0171898 0.0036628 -0.128277 -0.137534 1.34912
2 35.149 4.99329 -1.21156 -1.18458 -0.259614 -0.271509 0.367284 6 -0.242639 -0.237235 -0.0519926 -0.0543748 1.02278 -0.494619 -0.483603 -0.105987 -0.110843 0.149943
3 59.6951 29.5314 6.74816 7.00539 0.437645 0.363396 10.3113 35 0.228508 0.237218 0.0148196 0.0123054 0.963282 1.14065 1.18413 0.0739754 0.0614251 1.74293
4 79.3204 6.89452 2.26546 2.35391 2.16716 2.25987 0.8887 8 0.328588 0.341417 0.314331 0.327777 0.962424 0.80096 0.832232 0.766207 0.798983 0.314203
5 175.433 77.4359 37.0155 37.2683 0.397573 0.521928 4.95044 79 0.478015 0.481279 0.00513422 0.00674012 0.993217 4.16457 4.19301 0.0447304 0.0587214 0.556968
6 271.249 672.513 266.694 269.177 2.1845 2.63223 58.935 707 0.396564 0.400256 0.00324827 0.00391403 0.990776 10.0301 10.1235 0.0821567 0.0989953 2.21648
7 445.262 1994.76 440.322 443.662 -0.547523 -0.016523 622.362 2001 0.220739 0.222414 -0.00027448 -8.28321e-06 0.992472 9.84345 9.91811 -0.0122399 -0.000369374 13.913
8 734.109 4731.35 588.933 592.559 -3.53957 -3.83589 2942.21 4765 0.124475 0.125241 -0.00074811 -0.000810739 0.993881 8.53168 8.5842 -0.0512766 -0.0555693 42.6229
9 1213.44 12251.5 840.941 847.877 -6.93399 -6.88018 10578.3 12232 0.0686398 0.069206 -0.000565971 -0.000561578 0.991819 7.60355 7.66627 -0.0626953 -0.0622087 95.6463
10 1742.09 11141.8 435.075 437.388 13.9856 12.8192 11723.8 11073 0.0390489 0.0392566 0.00125523 0.00115055 0.994711 4.13458 4.15657 0.132907 0.121823 111.413
In [71]:
# why some eT values are -ve?
"""
1. For given rmin and dlnr we have some bins very few object counts.

""";
In [72]:
pd.cut(df['eT_mono'],20).value_counts()
Out[72]:
(0.00144, 0.108]     14304
(0.108, 0.214]        6224
(-0.105, 0.00144]     3129
(0.214, 0.32]         2270
(0.32, 0.426]         1178
(-0.211, -0.105]       934
(0.426, 0.533]         643
(-0.317, -0.211]       508
(-0.424, -0.317]       418
(0.533, 0.639]         402
(-0.53, -0.424]        323
(-0.636, -0.53]        229
(0.639, 0.745]         169
(-0.742, -0.636]       111
(-0.848, -0.742]        30
(0.745, 0.851]          30
(-0.957, -0.848]         6
(0.851, 0.958]           6
(1.064, 1.17]            2
(0.958, 1.064]           0
Name: eT_mono, dtype: int64
In [73]:
fig,ax = plt.subplots(figsize=(12,8))
sns.distplot(df['eT_mono'],ax=ax)
plt.title('Histogram and density plot of eT_mono');
In [74]:
df['wt_mag'].hist(bins=100,figsize=(12,8));
plt.title('Histogram of wt_mag')
plt.xlabel('wt_mag')
plt.ylabel('Frequency');
plt.savefig('images/weights.png',dpi=300)
In [75]:
df.query(""" r>500 """)['eT_mono'].describe()
Out[75]:
count    28553.000000
mean         0.065416
std          0.170729
min         -0.954698
25%          0.019631
50%          0.068047
75%          0.126914
max          1.170045
Name: eT_mono, dtype: float64
In [76]:
df['gm_sq'].hist(bins=100,figsize=(12,8))
plt.title('Histogram of gm_sq')
plt.ylabel('Frequency')
plt.xlabel('gm_sq')
plt.savefig('images/gm_sq_hist_after_cleaning.png',dpi=300)

Plot of eT for mono and chro

In [112]:
def plot_eT_mean(rmin, dlnr,min_bin_count,
                 show_ratio=True,
                 show_mono_chro=False,
                 show_data=True):
    # title
    title = f'rmin={rmin}, dlnr={dlnr}, min_bin_count={min_bin_count}'
    
    # radial bin
    df['bin'] = ( np.log(df.r / rmin) / dlnr).astype(int)

    # aggregations per given bin
    df_radial_bins = df.groupby('bin').agg(
        r_mean               = ('r', 'mean'),
        wt_mag_sum           = ('wt_mag', 'sum'),
        eT_mono_times_wt_sum = ('eT_mono_times_wt', 'sum'),
        eT_chro_times_wt_sum = ('eT_chro_times_wt', 'sum'),
        eX_mono_times_wt_sum = ('eX_mono_times_wt', 'sum'),
        eX_chro_times_wt_sum = ('eX_chro_times_wt', 'sum'),
        err_numerator_sum    = ('err_numerator', 'sum')
                                           )
    # bin counts
    df_radial_bins['bin_count'] = df['bin'].value_counts()
    df_radial_bins = df_radial_bins.query(""" bin_count > @min_bin_count """)  

    # columns after binning 
    df_radial_bins = df_radial_bins.eval("""
        eT_mean_mono = eT_mono_times_wt_sum / wt_mag_sum
        eT_mean_chro = eT_chro_times_wt_sum / wt_mag_sum
        eX_mean_mono = eX_mono_times_wt_sum / wt_mag_sum
        eX_mean_chro = eX_chro_times_wt_sum / wt_mag_sum
        eT_ratio = eT_mean_mono / eT_mean_chro
        """
    )
    
    # Errors
    b = np.sqrt(df_radial_bins['bin_count'])
    df_radial_bins['eT_mono_err'] = df_radial_bins['eT_mono_times_wt_sum'] / b
    df_radial_bins['eT_chro_err'] = df_radial_bins['eT_chro_times_wt_sum'] / b
    df_radial_bins['eX_mono_err'] = df_radial_bins['eX_mono_times_wt_sum'] / b
    df_radial_bins['eX_chro_err'] = df_radial_bins['eX_chro_times_wt_sum'] / b
    df_radial_bins['eT_ratio_err'] = df_radial_bins['err_numerator_sum'] / b

    
  
 
    # also plot eT mono and eT chro
    if show_ratio:
        fig, ax = plt.subplots(1,1,figsize=(12,8))
        df_radial_bins.plot.line(x='r_mean',y='eT_ratio',
                                 yerr='eT_ratio_err',
                                 marker='o',color='b',ax=ax)
        ax.set_xlabel('Radius',fontsize=18)
        ax.set_ylabel(r'$\frac{eT_{mono}}{eT_{chro}}$',fontsize=18)
        
    if show_mono_chro:
        fig, ax = plt.subplots(3,1,figsize=(14,12))
        
        # top
        df_radial_bins.plot.line(x='r_mean',y='eT_mean_mono',
                                 xerr='eT_mono_err', yerr='eX_mono_err',
                                 marker='o',color='r', ax=ax[0])
        
        # top
        df_radial_bins.plot.line(x='r_mean',y='eT_mean_chro',
                                 xerr='eT_chro_err', yerr='eX_chro_err',
                                 marker='o',color='b',ax=ax[0])
        # middle
        df_radial_bins.plot.line(x='r_mean',y='eT_mean_mono',
                                 xerr='eT_mono_err', yerr='eX_mono_err',
                                 marker='o',color='r', ax=ax[1])
        
        # bottom
        df_radial_bins.plot.line(x='r_mean',y='eT_mean_chro',
                                 xerr='eT_chro_err', yerr='eX_chro_err',
                                 marker='o',color='b',ax=ax[2])
        
        # label
        ax[0].set_xlabel('')
        ax[1].set_xlabel('')
        ax[2].set_xlabel('Radius',fontsize=18)
        ax[0].set_ylabel('eT',fontsize=18)
        ax[1].set_ylabel('eT_mean_mono',fontsize=18)
        ax[2].set_ylabel('eT_mean_chro',fontsize=18)

    plt.suptitle(f'Plot of eT for {title}',fontsize=24,weight='bold')
    
    # also show the dataframe
    if show_data:
        display(df_radial_bins.style.background_gradient(subset=['eT_mean_mono']))
    
    plt.tight_layout()
    plt.savefig('images/eT_versus_radius.png',dpi=300)
    plt.show()

# plot now
# show_ratio = False
# show_mono_chro = True
show_ratio = True
show_mono_chro = False
rmin = 300
dlnr = 0.5
min_bin_count = 10

plot_eT_mean(rmin=rmin, dlnr=dlnr,min_bin_count=min_bin_count,
            show_ratio=show_ratio,
            show_mono_chro=show_mono_chro)
r_mean wt_mag_sum eT_mono_times_wt_sum eT_chro_times_wt_sum eX_mono_times_wt_sum eX_chro_times_wt_sum err_numerator_sum bin_count eT_mean_mono eT_mean_chro eX_mean_mono eX_mean_chro eT_ratio eT_mono_err eT_chro_err eX_mono_err eX_chro_err eT_ratio_err
bin
-3 54.8887 23.2027 4.70387 4.91589 0.935191 0.897974 8.58784 26 0.20273 0.211867 0.0403053 0.0387013 0.956871 0.922504 0.964085 0.183406 0.176107 1.68421
-2 74.3131 13.5852 4.37844 4.49987 1.66208 1.71237 2.70816 18 0.322296 0.331234 0.122345 0.126047 0.973015 1.03201 1.06063 0.391756 0.40361 0.638319
-1 163.969 48.6491 23.9145 24.2543 1.65366 1.76361 3.50727 46 0.491571 0.498556 0.0339917 0.0362517 0.98599 3.526 3.5761 0.243819 0.260031 0.517119
0 366.792 2155.15 624.291 629.314 -0.116731 0.620806 348.208 2200 0.289674 0.292005 -5.41637e-05 0.000288057 0.992018 13.3099 13.417 -0.00248871 0.0132356 7.42383
1 665.863 4006.43 553.774 556.817 -0.0300627 -0.658032 2853.19 4022 0.138221 0.138981 -7.5036e-06 -0.000164244 0.994535 8.73195 8.77993 -0.000474031 -0.0103759 44.9893
2 1099.56 10071.8 789.434 795.835 -8.82913 -7.18731 7836.44 10089 0.0783806 0.079016 -0.000876618 -0.000713606 0.991958 7.85945 7.92317 -0.087901 -0.0715553 78.018
3 1657.62 14392.9 613.727 617.924 15.3237 13.1724 14672.1 14324 0.0426411 0.0429326 0.00106467 0.000915201 0.993209 5.12794 5.16301 0.128036 0.11006 122.592
4 2259.58 194.459 3.8408 3.78995 -2.4549 -2.47068 217.131 176 0.0197512 0.0194897 -0.0126243 -0.0127054 1.01342 0.289511 0.285678 -0.185045 -0.186235 16.3669

Interactive plots

In [78]:
import plotly.graph_objs as go
import plotly.figure_factory as ff
from plotly import tools
from plotly.offline import plot, iplot, init_notebook_mode
init_notebook_mode(connected=False)
In [79]:
df.filter(regex='wt').head(2)
Out[79]:
wt_mag_mono wt_mag_chro wt_mag eT_mono_times_wt eT_chro_times_wt eX_mono_times_wt eX_chro_times_wt eX_times_wt eX_chro_times_wt_std
0 1.704526 1.515862 1.610194 0.103431 0.098699 -0.069927 -0.077302 -0.073614 0.171205
2 0.305419 0.416606 0.361013 0.003071 -0.001150 0.021219 0.023631 0.022425 0.171205
In [94]:
def plotly_eT_plot(rmin=400, dlnr=0.4, min_bin=20,
                   show_mono_chro=False,
                   show_data=True):
    
    # title
    title=f'rmin={rmin}, dlnr={dlnr}, min_bin={min_bin}'
    
    # radial bin
    df['bin'] = ( np.log(df.r / rmin) / dlnr).astype(int)

    # aggregations per given bin
    df_radial_bins = df.groupby('bin').agg(
        r_mean               = ('r', 'mean'),
        wt_mag_sum           = ('wt_mag', 'sum'),
        eT_mono_times_wt_sum = ('eT_mono_times_wt', 'sum'),
        eT_chro_times_wt_sum = ('eT_chro_times_wt', 'sum'),
        eX_mono_times_wt_sum = ('eX_mono_times_wt', 'sum'),
        eX_chro_times_wt_sum = ('eX_chro_times_wt', 'sum'),
        err_numerator_sum    = ('err_numerator', 'sum')
    )
        
    # bin counts
    df_radial_bins['bin_count'] = df['bin'].value_counts()
    df_radial_bins = df_radial_bins.query(""" bin_count > @min_bin """)

    # columns after binning 
    df_radial_bins = df_radial_bins.eval("""
        eT_mean_mono = eT_mono_times_wt_sum / wt_mag_sum
        eT_mean_chro = eT_chro_times_wt_sum / wt_mag_sum
        eX_mean_mono = eX_mono_times_wt_sum / wt_mag_sum
        eX_mean_chro = eX_chro_times_wt_sum / wt_mag_sum
        eT_ratio = eT_mean_mono / eT_mean_chro
        """
    )
    
    # Errors
    b = np.sqrt(df_radial_bins['bin_count'])
    df_radial_bins['eT_mono_err'] = df_radial_bins['eT_mono_times_wt_sum'] / b
    df_radial_bins['eT_chro_err'] = df_radial_bins['eT_chro_times_wt_sum'] / b
    df_radial_bins['eX_mono_err'] = df_radial_bins['eX_mono_times_wt_sum'] / b
    df_radial_bins['eX_chro_err'] = df_radial_bins['eX_chro_times_wt_sum'] / b
    df_radial_bins['eT_ratio_err'] = df_radial_bins['err_numerator_sum'] / b    
    
    # eT mono vs chro ratio
    sc = go.Scatter( x=df_radial_bins['r_mean'],
                     y=df_radial_bins['eT_ratio'],
                     mode = 'lines+markers',
                     name = 'eT ratio',
                     error_y = dict(
                         type='data',
                         array=df_radial_bins['eT_ratio_err'],
                         visible=True,
                         )
                   )
    
    mydata = [sc]
    
    # also plot eT mono and chro
    if show_mono_chro:
        # monochromatic
        sc1 = go.Scatter(x=df_radial_bins['r_mean'],
                         y=df_radial_bins['eT_mean_mono'],
                         mode = 'lines+markers',
                         name = 'eT mono',
                         error_x = dict(
                             type='data',
                             array=df_radial_bins['eT_mono_err'],
                             visible=True,
                             ),
                         error_y = dict(
                             type='data',
                             array=df_radial_bins['eX_mono_err'],
                             visible=True,
                             )
                        )
        # chromatic
        sc2 = go.Scatter(x=df_radial_bins['r_mean'],
                         y=df_radial_bins['eT_mean_chro'],
                         mode = 'lines+markers',
                         name = 'eT chro',
                         error_x = dict(
                             type='data',
                             array=df_radial_bins['eT_chro_err'],
                             visible=True,
                             ),
                         error_y = dict(
                             type='data',
                             array=df_radial_bins['eX_chro_err'],
                             visible=True,
                             )
                        )

        mydata= [sc1,sc2]
    
    # layout
    layout = go.Layout(
                    title=title,
                    xaxis=dict(
                               title='radius',
                               titlefont=dict(
                               family='Courier New, monospace',
                               size=18,
                               color='#7f7f7f')),
                     yaxis=dict(title='eT',
                                titlefont=dict(
                                          family='Courier New, monospace',
                                          size=18,
                                          color='#7f7f7f')))
    
    myfig = go.Figure(data=mydata, layout=layout)
    
    myfig.update_layout(showlegend=True)

    
    # also show the dataframe
    if show_data:
        display(df_radial_bins.style.background_gradient(subset=['eT_mean_mono']))

    # iplot plots in jupyter-notebook, plot opens in new tab.
    return iplot(myfig, filename='myplot.html')

# plot
rmin = 300
dlnr = 0.5
min_bin = 20
plotly_eT_plot(rmin=rmin, dlnr=dlnr,min_bin=min_bin,show_mono_chro=True)
r_mean wt_mag_sum eT_mono_times_wt_sum eT_chro_times_wt_sum eX_mono_times_wt_sum eX_chro_times_wt_sum err_numerator_sum bin_count eT_mean_mono eT_mean_chro eX_mean_mono eX_mean_chro eT_ratio eT_mono_err eT_chro_err eX_mono_err eX_chro_err eT_ratio_err
bin
-3 54.8887 23.2027 4.70387 4.91589 0.935191 0.897974 8.58784 26 0.20273 0.211867 0.0403053 0.0387013 0.956871 0.922504 0.964085 0.183406 0.176107 1.68421
-1 163.969 48.6491 23.9145 24.2543 1.65366 1.76361 3.50727 46 0.491571 0.498556 0.0339917 0.0362517 0.98599 3.526 3.5761 0.243819 0.260031 0.517119
0 366.792 2155.15 624.291 629.314 -0.116731 0.620806 348.208 2200 0.289674 0.292005 -5.41637e-05 0.000288057 0.992018 13.3099 13.417 -0.00248871 0.0132356 7.42383
1 665.863 4006.43 553.774 556.817 -0.0300627 -0.658032 2853.19 4022 0.138221 0.138981 -7.5036e-06 -0.000164244 0.994535 8.73195 8.77993 -0.000474031 -0.0103759 44.9893
2 1099.56 10071.8 789.434 795.835 -8.82913 -7.18731 7836.44 10089 0.0783806 0.079016 -0.000876618 -0.000713606 0.991958 7.85945 7.92317 -0.087901 -0.0715553 78.018
3 1657.62 14392.9 613.727 617.924 15.3237 13.1724 14672.1 14324 0.0426411 0.0429326 0.00106467 0.000915201 0.993209 5.12794 5.16301 0.128036 0.11006 122.592
4 2259.58 194.459 3.8408 3.78995 -2.4549 -2.47068 217.131 176 0.0197512 0.0194897 -0.0126243 -0.0127054 1.01342 0.289511 0.285678 -0.185045 -0.186235 16.3669
In [89]:
# plot
rmin = 400
dlnr = 0.5
min_bin = 20
plotly_eT_plot(rmin=rmin, dlnr=dlnr,min_bin=min_bin,show_mono_chro=True)
r_mean wt_mag_sum eT_mono_times_wt_sum eT_chro_times_wt_sum eX_mono_times_wt_sum eX_chro_times_wt_sum err_numerator_sum bin_count eT_mean_mono eT_mean_chro eX_mean_mono eX_mean_chro eT_ratio eT_mono_err eT_chro_err eX_mono_err eX_chro_err eT_ratio_err
bin
-3 68.3757 28.0714 7.99462 8.36644 2.85206 2.86193 9.19808 32 0.284796 0.298042 0.1016 0.101952 0.955559 1.41326 1.47899 0.504178 0.505922 1.62601
-1 209.834 244.65 114.937 115.339 -1.75793 -1.7308 13.671 244 0.469802 0.471444 -0.00718547 -0.00707461 0.996517 7.35809 7.38381 -0.11254 -0.110803 0.875198
0 477.506 3811.59 826.374 833.813 5.24721 5.04126 1036.18 3853 0.216806 0.218757 0.00137664 0.00132261 0.991079 13.313 13.4329 0.0845335 0.0812156 16.6931
1 888.212 6737.46 670.115 673.355 -0.72371 1.30428 4696.85 6781 0.0994611 0.0999421 -0.000107416 0.000193586 0.995188 8.13772 8.17707 -0.00878856 0.0158388 57.0374
2 1443.99 16272.2 879.619 887.584 -24.9054 -26.2678 15549.2 16221 0.0540567 0.0545462 -0.00153055 -0.00161428 0.991026 6.90646 6.969 -0.195549 -0.206246 122.087
3 1969.56 3796.39 114.092 113.83 27.2726 26.3956 4633.09 3752 0.0300527 0.0299838 0.00718382 0.0069528 1.0023 1.86261 1.85835 0.445241 0.430923 75.6378

ipywidgets

which pip
pip install ipywidgets
jupyter nbextension enable --py --sys-prefix widgetsnbextension
In [82]:
import ipywidgets as widgets
from ipywidgets import HBox, VBox
from ipywidgets import interactive
In [113]:
rmin_ = widgets.IntSlider(min=0, max=500, step=50, value=300)
dlnr_  = widgets.FloatSlider(min=0.1,max=0.8,step=0.05,value=0.5)
min_bin_count_ = widgets.IntSlider(min=10, max=600, step=20, value=50)
interactive_plot = interactive(plotly_eT_plot,
                               rmin=rmin_,
                               dlnr=dlnr_,
                               min_bin_count=min_bin_count_)

output = interactive_plot.children[-1]
interactive_plot

Time Taken

In [84]:
time_taken = time.time() - time_start_notebook
h,m = divmod(time_taken,60*60)
print('Time taken to run whole notebook: {:.0f} hr '\
      '{:.0f} min {:.0f} secs'.format(h, *divmod(m,60)))
Time taken to run whole notebook: 0 hr 0 min 24 secs
In [85]:
import subprocess
subprocess.call(['python', '-m', 'nbconvert', '*.ipynb'])
Out[85]:
0